"While he is disappointed by the circumstances he finds himself in, he is hopeful that the truth will be known and he will be able to come home very soon," Hekmati's mother said in a statement, according to The Times. She described the Iranian officials she met as "hospitable" and "respectful," but said her son looked thinner and shocked by his ordeal.

Hekmati's family has publicly maintained Hekmati's innocence, as first voiced by his father to ABC News in an exclusive interview before the death sentence came down.

"My son is no spy. He is innocent. He's a good fellow, a good citizen, a good man," Hekmati said in December. "These are all unfounded allegations and a bunch of lies."

Hekmati, an Arizona-born Iranian-American who served the U.S. Marines as a rifleman from 2001 to 2005, was arrested while visiting his extended family, including two elderly grandmothers, in Tehran on Aug. 29, 2011, according to the family. The family said they were urged by the Iranian government to keep quiet about his arrest with the promise of later release, but then in December, Hekmati was shown on Iranian television allegedly confessing to being an undercover agent of the Central Intelligence Agency on a mission to infiltrate the Iranian Intelligence Ministry.

"It was their [the CIA's] plan to first burn some useful information, give it to them [the Iranians] and let Iran's Intelligence Ministry think that this is good material," Hekmati says calmly in the video.

Contrary to claims made during the initial Iranian broadcast, Hekmati's military record, provided to ABC News, shows that he never had intelligence training and the U.S. State Department said in early January Iran's claims that Hekmati "either worked for, or was sent to Iran by the CIA are simply untrue."

"The Iranian regime has a history of falsely accusing people of being spies, of eliciting forced confessions, and of holding innocent Americans for political reasons," State Department spokesperson Victoria Nuland said then.

With the exception of the rare family statement criticizing Iran's previous lack of cooperation, Hekmati's kin, now represented by a high-powered attorney and a public relations firm, have been quiet in their dogged efforts to free the 28-year-old.

"By remaining discreet, you are not ruling out the option to be more public later," the family's lawyer in America, Pierre-Richard Prosper, told The Times. "A more visible campaign has not been ruled out."

Shortly before Benhaz's visit, Hekmati's lawyers in Tehran filed an appeal with courts in Tehran.

Eric Volz, a spokesperson for the family, did not immediately respond to ABC News' request for comment on this report, but Volz confirmed Hekmati's mother's visit to The Associated Press. A website set up by representatives of the family, FreeAmir.org, posted The New York Times' story in place of a new family statement.